Definition:Connected (Topology)/Points

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $a, b \in S$.

Then $a$ and $b$ are connected (in $T$) if and only if there exists a connected set in $T$ containing both $a$ and $b$.

Also see

• Equivalence of Definitions of Connected Topological Space for a series of equivalent definitions for connectedness.

• Results about connected spaces can be found here.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $4$: Connectedness